Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.552356514044575744.1	x^16 - 2x^15 + x^14 - 2x^13 + 5x^12 - 10x^11 + 28x^10 - 40x^9 + 45x^8 - 38x^7 + 42x^6 - 16x^5 + 8x^4 + 8x^3 + 12x^2 + 4x + 1	\( 2^{24}\cdot 7^{6}\cdot 23^{4} \)	16T1025	Trivial
16.0.552356514044575744.2	x^16 - 6x^15 + 23x^14 - 62x^13 + 133x^12 - 226x^11 + 308x^10 - 328x^9 + 261x^8 - 138x^7 + 22x^6 + 28x^5 - 24x^4 + 4x^3 + 4x^2 + 1	\( 2^{24}\cdot 7^{6}\cdot 23^{4} \)	16T1025	Trivial
16.0.921677784681222144.1	x^16 - x^15 - 4x^14 - 3x^13 + 23x^12 + x^11 - 44x^10 + 3x^9 + 52x^8 - 3x^7 - 44x^6 - x^5 + 23x^4 + 3x^3 - 4x^2 + x + 1	\( 2^{12}\cdot 3^{14}\cdot 19^{6} \)	16T1025	Trivial (GRH)
16.4.1420005889600000000.1	x^16 - 4x^14 - 4x^12 - 10x^11 + 5x^10 - 15x^9 - 15x^8 + 10x^7 - 15x^6 + 15x^5 + 6x^4 - 10x^3 + 9x^2 - 5x + 1	\( 2^{12}\cdot 5^{8}\cdot 31^{6} \)	16T1025	Trivial
16.4.2069703095939497984.4	x^16 - 8x^14 + 26x^12 - 44x^10 + 35x^8 + 4x^6 - 18x^4 - 4x^2 + 1	\( 2^{44}\cdot 7^{6} \)	16T1025	Trivial
16.0.9440732714731831296.6	x^16 - 6x^15 + 14x^14 - 12x^13 + 10x^12 - 114x^11 + 452x^10 - 930x^9 + 1219x^8 - 1122x^7 + 788x^6 - 450x^5 + 214x^4 - 84x^3 + 26x^2 - 6x + 1	\( 2^{24}\cdot 3^{14}\cdot 7^{6} \)	16T1025	Trivial
16.8.142158742435915628544.1	x^16 - 10x^14 + 43x^12 - 118x^10 + 193x^8 - 184x^6 + 124x^4 - 64x^2 + 16	\( 2^{24}\cdot 3^{14}\cdot 11^{6} \)	16T1025	Trivial
16.4.142158742435915628544.2	x^16 + 2x^14 + x^12 + 14x^10 - 32x^8 + 26x^6 + 13x^4 - 10x^2 + 1	\( 2^{24}\cdot 3^{14}\cdot 11^{6} \)	16T1025	Trivial
16.4.142158742435915628544.3	x^16 - 2x^14 + x^12 - 14x^10 - 32x^8 - 26x^6 + 13x^4 + 10x^2 + 1	\( 2^{24}\cdot 3^{14}\cdot 11^{6} \)	16T1025	Trivial
16.0.142158742435915628544.4	x^16 + 10x^14 + 43x^12 + 118x^10 + 193x^8 + 184x^6 + 124x^4 + 64x^2 + 16	\( 2^{24}\cdot 3^{14}\cdot 11^{6} \)	16T1025	$[2]$
16.8.1917481604731113570304.6	x^16 - 8x^14 + 56x^10 + 30x^8 + 56x^6 - 8x^2 + 1	\( 2^{38}\cdot 17^{8} \)	16T1025	Trivial (GRH)
16.4.1917481604731113570304.10	x^16 - 6x^14 + 23x^12 - 52x^10 + 83x^8 - 150x^6 - 15x^4 + 48x^2 + 4	\( 2^{38}\cdot 17^{8} \)	16T1025	$[2]$
16.4.1917481604731113570304.11	x^16 + 8x^14 + 8x^12 - 24x^10 - 18x^8 - 24x^6 + 8x^4 + 8x^2 + 1	\( 2^{38}\cdot 17^{8} \)	16T1025	Trivial
16.0.1917481604731113570304.16	x^16 + 8x^14 + 38x^12 + 116x^10 + 229x^8 + 292x^6 + 220x^4 + 80x^2 + 4	\( 2^{38}\cdot 17^{8} \)	16T1025	$[2]$
16.0.114523100106217078515625.3	x^16 - 5x^15 + 23x^14 - 40x^13 + 115x^12 - 42x^11 + 462x^10 + 340x^9 + 1515x^8 + 1563x^7 + 3106x^6 + 2475x^5 + 2795x^4 + 1247x^3 + 922x^2 + 143x + 121	\( 5^{8}\cdot 29^{6}\cdot 149^{4} \)	16T1025	$[2, 8]$ (GRH)
16.8.114523100106217078515625.3	x^16 - x^15 - 12x^14 + 4x^13 + 73x^12 + 93x^11 - 406x^10 - 628x^9 + 954x^8 + 3578x^7 - 3729x^6 - 5634x^5 + 7966x^4 - 995x^3 - 1637x^2 + 253x + 121	\( 5^{8}\cdot 29^{6}\cdot 149^{4} \)	16T1025	Trivial (GRH)
16.0.71576937566385674072265625.1	x^16 - 4x^15 - 24x^14 + 104x^13 + 240x^12 - 1170x^11 - 1220x^10 + 5202x^9 + 11672x^8 - 5738x^7 - 85302x^6 - 52280x^5 + 288522x^4 + 344642x^3 - 39434x^2 + 310669x + 1680101	\( 5^{12}\cdot 29^{6}\cdot 149^{4} \)	16T1025	$[2, 28]$ (GRH)
16.8.71576937566385674072265625.1	x^16 - 4x^15 - 24x^14 + 104x^13 - 90x^12 - 330x^11 + 3270x^10 - 5798x^9 + 4472x^8 + 7302x^7 - 75142x^6 + 122230x^5 - 121338x^4 - 36648x^3 + 208986x^2 + 120019x + 18301	\( 5^{12}\cdot 29^{6}\cdot 149^{4} \)	16T1025	Trivial (GRH)
16.8.182182440601540289016015625.1	x^16 - 14x^14 + 153x^12 - 1870x^10 + 13060x^8 - 59643x^6 + 185825x^4 - 253602x^2 + 116281	\( 5^{8}\cdot 29^{6}\cdot 941^{4} \)	16T1025	Trivial (GRH)
16.8.182182440601540289016015625.2	x^16 - 2x^15 - 13x^14 + 49x^13 - 87x^12 - 83x^11 + 17x^10 - 1160x^9 + 3440x^8 + 5130x^7 - 8386x^6 - 20986x^5 + 33570x^4 + 67832x^3 - 73866x^2 - 106436x - 10211	\( 5^{8}\cdot 29^{6}\cdot 941^{4} \)	16T1025	Trivial (GRH)
16.16.445043617281809103797265625.1	x^16 - x^15 - 52x^14 + 94x^13 + 795x^12 - 1606x^11 - 5326x^10 + 10959x^9 + 17153x^8 - 34309x^7 - 25896x^6 + 48486x^5 + 15590x^4 - 26274x^3 - 4037x^2 + 4031x + 841	\( 5^{8}\cdot 101^{6}\cdot 181^{4} \)	16T1025	Trivial (GRH)
16.16.445043617281809103797265625.2	x^16 - 4x^15 - 43x^14 + 183x^13 + 604x^12 - 2965x^11 - 3076x^10 + 22224x^9 - 1106x^8 - 79258x^7 + 56447x^6 + 113174x^5 - 146225x^4 - 14427x^3 + 93070x^2 - 44937x + 6259	\( 5^{8}\cdot 101^{6}\cdot 181^{4} \)	16T1025	Trivial (GRH)
16.0.152641787400686250102941024256.6	x^16 + 44x^14 + 688x^12 + 5228x^10 + 20998x^8 + 43556x^6 + 40048x^4 + 9380x^2 + 529	\( 2^{54}\cdot 3^{14}\cdot 11^{6} \)	16T1025	$[4, 4, 48]$ (GRH)
16.0.152641787400686250102941024256.7	x^16 + 28x^14 + 268x^12 + 1204x^10 + 2818x^8 + 3484x^6 + 2116x^4 + 484x^2 + 1	\( 2^{54}\cdot 3^{14}\cdot 11^{6} \)	16T1025	$[2, 12, 36]$ (GRH)
16.0.11939508427262544380953600000000.1	x^16 - 2x^15 + 113x^14 - 170x^13 + 5670x^12 - 5200x^11 + 162976x^10 - 45672x^9 + 2933108x^8 + 851928x^7 + 34322677x^6 + 21797522x^5 + 263102522x^4 + 148225950x^3 + 1229052881x^2 + 112463354x + 2667232231	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{4} \)	16T1025	$[4, 37960]$ (GRH)
16.0.11939508427262544380953600000000.2	x^16 - 2x^15 + 113x^14 - 172x^13 + 5830x^12 - 6642x^11 + 175264x^10 - 161942x^9 + 3284104x^8 - 2727984x^7 + 38554411x^6 - 29815402x^5 + 273976211x^4 - 167301256x^3 + 1092003662x^2 - 247972336x + 2265405829	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{4} \)	16T1025	$[4, 36920]$ (GRH)